Neural Control of Neutralization Process using …...pH neutralization process involves material balance on selective ions, equilibrium constants and electroneutrality equation [1]

International Journal of Computer Applications (0975 – 8887)

Volume 61– No.9, January 2013

16

Neural Control of Neutralization Process using Fuzzy

Inference System based Lookup Table

Parikshit Kishor Singh BITS Pilani, Pilani Campus

Dept. of EEE/INSTR Rajasthan-333031, India

Surekha Bhanot BITS Pilani, Pilani Campus

Dept. of EEE/INSTR Rajasthan-333031, India

Harekrishna Mohanta BITS Pilani, Pilani Campus Dept. of Chemical Engg. Rajasthan-333031, India

ABSTRACT

Over a number of years, pH control of neutralization process

is recognized as a benchmark for modeling and control of

nonlinear processes. This paper first describes dynamic

modeling of pH neutralization process. Thereafter fuzzy logic

based pH control scheme for neutralization process is

developed. Further, a two-dimensional (2-D) lookup table is

generated based on defuzzification mechanism of fuzzy

inference system (FIS). Finally, using this lookup table, a

neural network control for pH neutralization process is

developed. Performances of fuzzy logic based control and

lookup table based neural network control for servo and

regulatory operations are compared based on integral square

error (ISE) and integral absolute error (IAE) criterions.

Results indicate that lookup table based neural network

control performs better than fuzzy logic based control.

General Terms

Nonlinear process control, fuzzy logic control, neural network

control.

Keywords

Fuzzy logic, lookup table, neural network, neutralization

process, pH control.

1. INTRODUCTION Control of pH plays a pivotal role in many modern industrial

applications such as boiler feedwater treatment in thermal

power plant, wastewater treatment in paper and pulp industry,

biopharmaceutical manufacturing, and chemical processing.

However, due to high nonlinearity and time-varying

parameters, control of pH is difficult and demanding. Further,

modern process industries require more accurate, robust and

flexible control systems for efficient and reliable operations.

To meet these stringent demands, intelligent control strategies

are increasingly being employed in modern process industries.

Development of the first-principle based dynamic modeling of

pH neutralization process involves material balance on

selective ions, equilibrium constants and electroneutrality

equation [1]. The associated model has been used by

researchers as a platform for many subsequent investigations

and forms the basis to introduce new and improved forms of

dynamic modeling and pH control of neutralization process

using the concept of reaction invariant and strong acid

equivalent [2], [3]. Many different and practical approaches

for pH control based on feedforward and gain scheduling

techniques have also been proposed in the literature [4], [5],

[6], [7].

The term "fuzzy logic" gives an impression of vague logic. In

reality, the term "fuzzy logic" refers to the fact that that the

logic involved can deal with lexical definition of inputs, in

contrast to binary logic which accepts only "true" or "false".

Therefore, the term "fuzzy" in fuzzy logic applies to the

imprecision in the data and not in the logic [8]. Fuzzy logic

based intelligent control can be described as a control

approach that is evolved based on experience and intuitive

understanding of process and is used to synthesize linguistic

control rules of a skilled operator. Since its origination, many

people from both academic and industrial communities have

devoted considerable effort for development of theoretical

research and application techniques on fuzzy logic [9], [10],

[11]. Literature review shows that application of fuzzy logic

to conventional control techniques such as PID control,

sliding mode control, and adaptive control, results in

improved performance for the hybrid controller over their

conventional counterparts [12], [13], [14].

A neural network can be considered as a computer program

that emulates the human brain and is designed to learn by

example and past experience. In past few decades, neural

networks based intelligent control techniques have received

great attention and undergone substantial development.

Because of its ability to handle nonlinearities, neural network

based model-free control techniques have provided promising

solutions for many nonlinear problems, especially in the field

of nonlinear chemical processes [15]. Finally, integration of

expert knowledge from fuzzy logic and adaptive learning

capabilities of neural network results in neuro-fuzzy control.

It has been recognized that the neuro-fuzzy control

techniques, such as adaptive network fuzzy inference system

(ANFIS), provides better control strategy [16].

2. DYNAMIC pH PROCESS MODEL The pH neutralization process takes place in continuous

stirred tank reactor (CSTR) with perfect mixing and constant

maximum volume. As shown in Fig. 1, the CSTR has two

influent streams: the hydrochloric acid as titration stream

(feed A) and the sodium hydroxide as process stream (feed

B), and one outlet stream: the effluent stream. The peristaltic

pumps A and B regulate the flow of feed A and feed B

respectively. The flow characteristics of peristaltic pumps A

and B are identical.

The dynamic model of pH neutralization process involves

material balances on selective ions, equilibrium relationship,

and electroneutrality equation. Based on principle of material

balances the process mixing dynamics may be described as

follows:

(1)

(2)

where is the maximum volume of the CSTR (1.9 L);

are the concentration (0.05 mol/L) and flow rate (0 to 6.23



17

mL/s) of titration stream A; are the concentration (0.05

mol/L) and flow rate (0 to 6.23 mL/s) of process stream B;

is the flow rate of effluent stream; is the

concentration of acid component (chloride ion, ) in the

effluent stream; is the concentration of base component

(sodium ion, ) in the effluent stream.

The equilibrium relationship for water is given as

(3)

where is the dissociation constant of water (10-14).

From the electroneutrality condition, we have

(4)

All of the comes from the and all of the comes

from the . Using (3) and (4), we have

(5)

From the definition of , the pH titration

curve for a strong acid-strong base is given by

(6)

where (7)

Fig. 1. pH Neutralization process

3. DESIGN OF FUZZY CONTROLLER The fuzzy logic based controller for pH neutralization process

is based on Mamdani FIS, most commonly used fuzzy

methodology [17], [18]. It consists of an input stage known as

fuzzifier, a processing stage known as fuzzy rule evaluator,

and an output stage known as defuzzifier. The fuzzifier stage

first determines the degree (a number between 0 and 1) to

which each input belong to the appropriate fuzzy sets via

membership functions. If the antecedent or premise (the IF-

part of the rule) of a given rule has more than one part, the

fuzzy operator is applied to obtain one number that represents

the result of the antecedent for that rule. The processing stage

first applies each rule's weight (a number between 0 and 1) to

the number given by corresponding antecedent. The

implication method is then applied on consequent or

conclusion (the THEN-part of the rule), a fuzzy set

represented by a membership function, of each rule. During

implication process, each individual consequent is reshaped

using the single number associated with the corresponding

antecedent. Finally, using aggregation process, the truncated

output functions are combined into a single fuzzy set. The

defuzzifier stage takes the aggregate output fuzzy set as input

and gives a single number as defuzzified output. The

Mamdani FIS used here assumes AND method for fuzzy

operator, unity weight for every rule, minimum method for

implication process, maximum method for aggregation

process, and centroid method for defuzzification process.

The input variables used for the fuzzy logic based controllers

are error (e) i.e. the difference between the desired (pHSP) and

measured (pH) values of control variable pH, and change in

error (ce) i.e. the difference between the error at the present

and previous instants. The output variable used for the fuzzy

logic based controller is the change in output (co) i.e. the

change in flow rate of feed A. The membership functions for

the input and output variables e, ce, and co are shown in Fig.

2, Fig. 3, and Fig. 4 respectively. The rule base for the input

and output variables are shown in Table I.

Fig. 2. Membership functions for error (e)

Fig. 3. Membership functions for change in error (ce)

Fig. 4. Membership functions for change in output (co)



18

Table I. Rule base for fuzzy logic control

ce

NL NM NS ZE PS PM PL

e

NL NL NL NL NL NM NS ZE

MN NL NL NL NM NS ZE PS

NS NL NL NM NS ZE PS PM

ZE NL NM NS ZE PS PM PL

PS NM NS ZE PS PM PL PL

PM NS ZE PS PM PL PL PL

PL ZE PS PM PL PL PL PL

NL = Negative Large, NM = Negative Medium, NS =

Negative Small, ZE = Zero, PS = Positive Small, PM =

Positive Medium, PL = Positive Large.

4. DESIGN OF LOOKUP TABLE BASED

NEURAL CONTROLLER The design of neural network controller for pH neutralization

process is carried out using a 2-D lookup table based on

previously defined FIS [18], [19]. The 9×9 lookup table is

generated by varying the input variables 'e', from -4 to 4 in

step of 1, and 'ce', from -0.5 to 0.5 in step of 0.125, and

computing the fuzzy logic output variable 'co' using centroid

method, as shown in Table II. The neural network utilizes

feedforward topology for its two layer architecture and back-

propagation learning algorithm for its training. The number of

neurons in input, hidden, and output layers are 2, 3, and 1

respectively. The activation function for both hidden as well

as output neurons is "purelin". For the neural network, the

training function is "traingdx", and the learning function is

"learngdm". Finally, mean square error (MSE) is chosen as

the performance function for the neural network. The 2-D

lookup table provides a set of 81 input and target data. Using

this data set, the neural network is being trained. The neural

network training parameters are: 5000 as the maximum

number of epochs, 10-12 as the performance goal, 10-10 as the

minimum performance gradient, 0.5 as the learning rate, and

0.9 as the momentum constant. For the neural network, the

training performance of 9.82×10-13 is obtained in 236 epochs,

and the regression value is 0.91, as shown in Fig. 5 and Fig. 6

respectively.

Fig. 5. Best training performance plot for the neural

network

Fig. 6. Linear regression plot for the neural network

5. RESULTS AND DISCUSSION The block diagram schematic of "intelligent" pH control of

neutralization process is shown in Fig. 7. The "intelligent"

controller block in the schematic diagram denotes either fuzzy

logic based controller or lookup table based neural controller.

Table II. Two-dimensional lookup table

ce

-0.5 -0.375 -0.25 -0.125 0 0.125 0.25 0.375 0.5

e

-4 -2.38×10-6 -2.38×10-6 -2.38×10-6 -2.38×10-6 -2.38×10-6 -1.68×10-6 -8.4×10-7 4.2×10-23 4.2×10-23

-3 -2.38×10-6 -2.38×10-6 -2.38×10-6 -2.38×10-6 -2.38×10-6 -1.68×10-6 -8.4×10-7 4.2×10-23 4.2×10-23

-2 -2.38×10-6 -2.38×10-6 -2.38×10-6 -2.38×10-6 -1.68×10-6 -8.4×10-7 4.2×10-23 8.4×10-7 8.4×10-7

-1 -2.38×10-6 -2.38×10-6 -2.38×10-6 -1.68×10-6 -8.4×10-7 4.2×10-23 8.4×10-7 1.68×10-6 1.68×10-6

0 -2.38×10-6 -2.38×10-6 -1.68×10-6 -8.4×10-7 4.2×10-23 8.4×10-7 1.68×10-6 2.38×10-6 2.38×10-6

1 -1.68×10-6 -1.68×10-6 -8.4×10-7 4.2×10-23 8.4×10-7 1.68×10-6 2.38×10-6 2.38×10-6 2.38×10-6

2 -8.4×10-7 -8.4×10-7 4.2×10-23 8.4×10-7 1.68×10-6 2.38×10-6 2.38×10-6 2.38×10-6 2.38×10-6

3 4.2×10-23 4.2×10-23 8.4×10-7 1.68×10-6 2.38×10-6 2.38×10-6 2.38×10-6 2.38×10-6 2.38×10-6

4 4.2×10-23 4.2×10-23 8.4×10-7 1.68×10-6 2.38×10-6 2.38×10-6 2.38×10-6 2.38×10-6 2.38×10-6



19

Fig. 7. "Intelligent" pH controller

The comparison of servo and regulatory response

characteristic terms, such as rise and fall time, settling time

(for ±1% error band), maximum overshoot and undershoot,

and decay ratio, for fuzzy logic based controller and lookup

table based neural network controller are carried out using

MATLAB simulation. To calculate overall performance

parameters ISE and IAE, all the errors with magnitude greater

than or equal to 0.01 are considered since further smaller

errors will have negligible contribution.

5.1 Servo operation For servo operation, as shown in Fig. 8, the pH set point

(pHSP) is varied from 7 to 10 in unit positive step at sampling

instants 500, 1000, and 2500 respectively; then from 10 to 4

in unit negative step at sampling instants 6000, 7500, 8000,

8500, 9000, and 10500 respectively; and finally from 4 to 7 in

unit positive step at sampling instants 14000, 15500, and

16000 respectively. The flow rate of process stream (Fb) is

kept constant at its nominal value of 1.75 mL/s. The resulting

variation of the controlled variable (pH) and manipulated

variable (Fa) for fuzzy logic based control and lookup table

based neural network control techniques are shown in Fig. 8

and Fig. 9 respectively.

From Fig. 8 and Fig. 9, it is evident that the pH neutralization

system response for lookup table based neural network

controller has little more rise and fall time; but much reduced

settling time, (maximum) overshoot and undershoot, and

decay ratio. The reason behind this is the loosely fitted neural

network with regression value of 0.91 only. In particular,

when the pH set point changes from 10 to 9 and from 4 to 5,

the servo response characteristic terms is compared for both

controllers, as shown in Table III and Table IV respectively.

For servo operation, the values of ISE and IAE for fuzzy logic

based control technique are 1580.54 and 1548.10 respectively,

whereas the corresponding values for lookup table based

neural network control technique are 831.62 and 1277.14

respectively. Finally, both fuzzy logic based control technique

as well as lookup table based neural network control

technique is able to track the set point variation with

negligible steady state error.

Fig. 8. pH variation due to servo operation

3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

8

8.5

9

9.5

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pH

Sample number

Set point

Fuzzy logic based control

Lookup table based neural network control



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Fig. 9. Acid flow rate variation due to servo operation

For servo operation, the values of ISE and IAE for fuzzy logic

based control technique are 1580.54 and 1548.10 respectively,

whereas the corresponding values for lookup table based

neural network control technique are 831.62 and 1277.14

respectively. Finally, both fuzzy logic based control technique

as well as lookup table based neural network control

technique is able to track the set point variation with

negligible steady state error.

TABLE III. Characteristic Comparison for Set Point

Change from 10 to 9

Fuzzy control Neural control

Fall time 106 samples 126 samples

Settling time 706 samples 476 samples

Maximum undershoot 3.94 3.24

Decay ratio 0.34 0.046

TABLE IV. Characteristic Comparison for Set Point

Change from 4 to 5


Rise time 106 samples 130 samples

Settling time 837 samples 637 samples

Maximum overshoot 3.99 3.27


5.2 Regulatory operation For regulatory operation, as shown in Fig. 11, the flow rate of

process stream (Fb) is subjected to pulse disturbance of

amplitude 1% of the nominal value and duration 200

samples at sampling instants 200 and 600 respectively; then of

amplitude 3% of the nominal value and duration 500

samples at sampling instants 1000 and 2000 respectively; and

finally of amplitude 5% of the nominal value and duration

1000 samples at sampling instants 3000 and 5000

respectively. The nominal flow rate of the process stream (Fb)

is taken as 1.75 mL/s. The pH set point is kept constant at 7.

The resulting variation of the controlled variable (pH) and

manipulated variable (Fa) for fuzzy logic based control and

lookup table based neural network control techniques are

shown in Fig. 10 and Fig. 11 respectively.

From Fig. 10 and Fig. 11, it is clear that, as compared to the

fuzzy logic based controller, the disturbance rejection is better

for lookup table based neural network controller. For step

disturbances of magnitude 5% of the nominal value at the

sampling instants 3000 and 5000 respectively, the comparison

of regulatory response characteristics for both controllers are

shown in Table V and Table VI respectively.

TABLE V. Characteristic Comparison for +5%

Magnitude Step Disturbance


Rejection time 337 samples 278 samples

Maximum undershoot 2.69 2.79


TABLE VI. Characteristic Comparison for -5%

Magnitude Step Disturbance


Rejection time 348 samples 283 samples

Maximum overshoot 2.69 2.78


1.7

1.71

1.72

1.73

1.74

1.75

1.76

1.77

1.78

1.79

1.8

1.81

1.82

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50

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Flo

w r

ate

(mL

/s)

Sample number





21

For regulatory operation, the values of ISE and IAE for fuzzy

logic based control technique are 7975.78 and 3958.21

respectively, whereas the corresponding values for lookup

table based neural network control technique are 7086.64 and

3433.00 respectively. Finally, both control techniques has

negligible steady state error for regulatory operation.

6. CONCLUSION Using a 2-D lookup table based on defuzzified FIS, a two

layered neural network based controller is designed and is

loosely trained to substitute the fuzzy logic based controller.

Based on ISE and IAE values, it can be concluded that the

proposed lookup table based neural network controller

performs better than fuzzy logic based controller for both

servo and regulatory operations. Also the steady state error

present in lookup table based neural network controller is not

appreciable and it can be neglected. To further improve the

controller performance, optimization techniques may be

applied.

Fig. 10. pH variation due to regulatory operation

Fig. 11. Acid flow rate variation due to regulatory operation

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pH

Sample number



1.58

1.6

1.62

1.64

1.66

1.68

1.7

1.72

1.74

1.76

1.78

1.8

1.82

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1.86

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1.92

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Flo

w r

ate

(mL

/s)

Sample number

Flow rate of process stream





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pH in controlled stirred tank reactor. Ind. Eng. Chem.

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and reaction invariant control of pH. Chemical

Engineering Science 38 (Mar. 1983), 389-398.

[3] Wright, R.A. and Kravaris, C. Nonlinear control of pH

processes using strong acid equivalent. Ind. Eng. Chem.

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[14] Daroogheh, N. 2009. High gain adaptive control of a

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[17] Mamdani, E.H. and Assilian, S. An experiment in

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Documents

Neural Control of Neutralization Process using …...pH neutralization process involves material balance on selective ions, equilibrium constants and electroneutrality equation [1]